LOCAL ANALYSIS APPROACH FOR SHORT WAVELENGTH VARIATIONS IN THE GEOPOTENTIAL

Bender, P. L. (1), and Wiese, D. N. (2)
(1) JILA, Univ. of Colorado and Nat. Inst. of Standards & Technology, Boulder, CO 80309, USA
(2) Dept. of Aerospace Engineering Science and Colorado Center for Astrodynamics Research, Univ. of Colorado, Boulder, CO 80309, USA

The value of global spherical harmonic analyses for determining 15 day to 30 day changes in the Earth's gravity field has been demonstrated extensively using data from the GRACE mission and previous missions. However, additional useful information appears to be obtainable from local analyses of the data. A number of such analyses have been carried out by various groups. In the energy approximation, the changes in the height of the satellite altitude geopotential can be determined from the post-fit changes in the satellite separation during individual one-revolution arcs of data from a GRACE-type pair of satellites in a given orbit. For a particular region, it is assumed that the arcs crossing that region during a time T of interest would be used to determine corrections to the spherical harmonic results. The shortest wavelengths that can be determined are the most important for investigating the spatial distribution of mass changes with high resolution.

While the longer wavelength variations are affected by mass distribution changes over much of the globe, the shorter wavelength ones hopefully will be determined mainly by more local changes in the mass distribution. The method of putting together results from different arcs crossing the region of interest with the energy approach has been used frequently before. It can be referred to as along-track analysis. The advantages of this approach can be seen most easily for an orbit with moderate inclination, such that the crossing angle between south-to-north (S-N) and N-S passes is fairly large over most regions well away from the poles. In that case, after filtering to pass the shorter wavelengths, the results for a given time interval can be combined to give the short wavelength W-E variations in the geopotential efficiently.

Questions have been raised about the effectiveness of local analyses, since changes in the geopotential at satellite altitude over a given region come from mass distribution changes over the whole globe. But, the main issue in considering higher measurement accuracy in future missions is how much improvement in spatial resolution can be achieved. For this, it is the shortest wavelengths in the geopotential spatial variations that are most important. To check on the effects of local versus global mass distribution changes, some preliminary calculations have been carried out for a roughly 2,000 by 2,000 km region in western and central North America. The results from these calculations indicate that most of the variations for wavelengths less than 1400 km will come from mass changes in the region considered.

Future missions are expected to have much higher accuracy for measuring changes in the satellite separation than GRACE. However, how large an improvement in the derived results in hydrology will be achieved is still very much a matter of study, because of the uncertainty in time variations in the atmospheric and oceanic mass distribution. To be specific, we will assume that improving the spatial resolution is the top objective, the satellite altitude is in the range of roughly 300 to 360 km made possible for long missions by drag-free operation, and ask first what information can be obtained for a single pass across a given Gaussian disk of water.

This single disk measure of performance is clearly much too optimistic because it ignores the complication of not knowing the geometry of the water distribution in the rest of the area of interest. However, it appears to give some insight into the spatial resolution issue, pending further studies. The major limitation is that the wavelengths of the variations in the satellite separation depend mainly on the altitude, until the half-thickness radius R of the disk becomes comparable with the altitude. Thus the measurement accuracy necessary in order to determine R is considerably higher than to just determine the total mass of the disk.

Some preliminary and approximate results will be given for both K-band and laser interferometer distance measurement systems, with and without some atmospheric mass variation uncertainty included. Although these results have been obtained only for a single pass across the region of interest, similar results for crossing S-N and N-S paths can be combined to give the short wavelength W-E variations when the crossing angles are fairly large. But more complete studies including information on expected patterns in the spatial distribution of the hydrological mass changes certainly are needed. A preliminary model probably would be uniform water depth changes in individual river basins. However, it is hoped that the resolution would be high enough to detect something like different changes in different distance ranges from the midlines of the basins, at least for the larger basins.